Turbomachines are used in myriad applications, including in air turbomachine starters used in aircraft engines. Typically, a turbomachine includes a turbomachine blade row comprised of a plurality of generally radially extending turbomachine airfoil members or airfoil members that are each mounted to an annular duct through which a compressible fluid flows. The airfoil members are spaced apart and positioned such that the annular duct rotates when a pressure differential is created across the two sides of the airfoils. Where a plurality of rows of airfoil members are formed, each row of aerofoil members divides the duct into a series of airfoil passages, each bounded by the facing suction and pressure surfaces of adjacent pairs of airfoil members in the row. Generally, each airfoil member is similarly sized and shaped.
During the engine operation, a three-dimensional flow in the airfoil passages represents a difficult problem in fluid mechanics. The flow field within the airfoil passages is complex and includes a number of secondary vortical flows which are a major source of energy loss. Reference can be made to Langston (1977) “Three-Dimensional Flow Within A Turbomachine Cascade Passage”, Transactions of the ASME, Journal of Engineering for Power, Vol. 99, pp 21-28 for a detailed discussion of these flows. The importance of these secondary flows increases with increase of aerodynamic duty or decrease in the aspect ratio of the airfoils. Not only is there energy dissipation in the secondary flows themselves, but they can also adversely affect the fluid flow downstream because they cause deviation of the angles of the flow exiting from the row of aerofoil members.
It has been found that an end wall of the turbine blade row to which the airfoil members are mounted and its boundary layers influence the formation of these secondary flows. Various attempts have been made in the past to modify the design of these turbomachines to eliminate these secondary vortical flows. For example, some designs include the addition of a fillet between the airfoil members and the end wall to reduce the secondary vortical flow generated from a blunt leading edge of the airfoils. Other designs reduce the secondary flow by compound leaning of the airfoil shape in a radial direction. Still other designs have re-shaped the end wall by applying varying functions in the axial direction and sloping the end wall in the circumferential or tangential direction
Although the above-mentioned modifications may address the formation of the secondary vortical air flows in the airfoil passages, they may not adequately reduce the secondary flow and are complex in calculation and achievement. Specifically, the past methods suggest solutions to mitigate current effects by relying on end wall modification based on multiple functions, rather than a simplified function that allows the modification of the end wall in both the circumferential and axial directions.
Therefore, there is a need for a simple method of modifying an end wall design and an end wall design that specifically addresses the secondary flow effects in the airfoil passages. The present invention addresses these needs.